For small holes in stainless ordinary HSS twist drills are fine, but avoid the very cheap ones. Stainless steel is quite abrasive on tools and conducts heat relatively poorly and cutting tools can tend to get hot, so the better quality HSS grades containing cobalt (eg M42) will tend to perform better.
You can get solid carbide drills which can be used for drilling very hard metals eg high alloy and tool steels. But these are brittle and easy to break so best suited for drilling machins with rigidly supported work.
Conventional spade bits aren't generally suitable for metalwork as they don't have the correct geometry although you can get counterbores for metal which perfom a similar function (ie producing a flat botomed hole).
Diamond coated tools are generally intended for very hard and brittle, friable materials like concrete, stone and ceramics, using them on ductile metals (like steels) will clog the diamond abrasive very quickly.
Coatings are primarily there to reduce friction and improve surface hardness of the drill, this is only really significant in deeper holes where chip clearance and binding in the hole are important factors.
Lubricant will help when drilling most metals (the main exception being cast iron), usually any light oil is fine although you can get specific cutting oils and pastes.
As a general rule of thumb twist drills are fine for holes of diameter up to about twice the thickness of the material being drilled. For much larger holes a step drill may perform better, although you need to take care not to allow a step drill to overheat, especially in stainless. For very large holes (more than about 20mm) a hole saw or sheet metal punch will give better results.
For thin sheet backing the hole with plywood or similar will help prevent the drill from tearing through the metal and jamming or forming a ragged hole as it breaks through the back side of the metal. Centre punching the hole location before you drill will also help to prevent the drill form wandering and reduces the risk of breaking bits.
Bear in mind also that with drills smaller than a few mm you are likely to break them fairly regularly so if you have a lot of one size to drill it is worth getting a pack of several of the same size. If you can find a specialist engineering tool retailer online these are often not very expensive for reasonable quality bits.
The drill speed should be matched to the diameter of the drill and the material being drilled, the easiest way to do this is to consult a reference chart although bear in mind that these figures can vary a bit depending on the precise conditions. For thin material you generally want to apply light pressure and use a failry high drill speed.
All twist drills will leave a slightly burred edge whatever you do, for the neatest results these can be cleaned up with a countersinking tool or a conical burr.
